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- W4295288949 abstract "Let $q>rge1$ be coprime positive integers. We empirically study the maximal gaps $G_{q,r}(x)$ between primes $p=qn+rle x$, $nin{mathbb N}$. Extensive computations suggest that almost always $G_{q,r}(x)<varphi(q)log^2x$. More precisely, the vast majority of maximal gaps are near a trend curve $T$ predicted using a generalization of Wolf's conjecture: $$G_{q,r}(x) ~sim~ T(q,x)={varphi(q)xover{rm li}(x)} Big(2log{{rm li}(x)overvarphi(q)} - log x + bBig),$$ where $b = b(q,x) = O_q(1)$. The distribution of properly rescaled maximal gaps $G_{q,r}(x)$ is close to the Gumbel extreme value distribution. However, the question whether there exists a limiting distribution of $G_{q,r}(x)$ is open. We discuss possible generalizations of Cramer's, Shanks, and Firoozbakht's conjectures to primes in residue classes." @default.
- W4295288949 created "2022-09-12" @default.
- W4295288949 creator A5014720932 @default.
- W4295288949 date "2016-10-10" @default.
- W4295288949 modified "2023-09-25" @default.
- W4295288949 title "On the distribution of maximal gaps between primes in residue classes" @default.
- W4295288949 doi "https://doi.org/10.48550/arxiv.1610.03340" @default.
- W4295288949 hasPublicationYear "2016" @default.
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